Geometric pumping and dephasing at topological phase transition

TL;DR

This paper introduces a formalism to analyze geometric pumping at topological phase transitions, revealing fractional, ceiling-limited pumping probabilities and conditions for occurrence linked to system dimension and number properties.

Contribution

It develops a measure-preserving formalism to analytically study pumping phenomena at topological phase transitions, highlighting geometric and fractional effects with new theoretical insights.

Findings

Pumping probability is geometric and fractional.

Pumping has a ceiling of 1/2.

Occurrence conditions depend on system dimension and number properties.

Abstract

A measure-preserving formalism (MPF) is constructed and applied to spin/band models, which yield observations about pumping. It occurs at topological phase transition (TPT), i.e., a $Z_2$-flip, suggesting that $Z_2$ can imply bulk effects. The model's asymptotic behavior is analytically solved via MPF. The pumping probability is geometric, fractional, and has a ceiling of $\frac{1}{2}$. Intriguingly, theorems are proved about occurrence conditions, which are linked to the system's dimension and the distinction between rational and irrational numbers. Experimental detection is discussed.